- #1
V0ODO0CH1LD
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I just got to a point in multivariable calculus where I realize I can solve problems in assignments and tests but have no actual idea of what I'm doing. So I started thinking about stuff and came up with a few questions:
1. Is picturing the derivative as the slope of the tangent line to a point of the graph just a useful analogy? Like imagining the integral is the area under the curve?
2. What is the meaning of taking the derivative of a vector? I get that you can take the derivative of each component separately with respect to a parameter that they all depend on. But what does that mean?
3. How is taking the derivative of a vector that describes a curve in space related to taking the derivative (or partial derivatives) of an equation that describes the same curve?
1. Is picturing the derivative as the slope of the tangent line to a point of the graph just a useful analogy? Like imagining the integral is the area under the curve?
2. What is the meaning of taking the derivative of a vector? I get that you can take the derivative of each component separately with respect to a parameter that they all depend on. But what does that mean?
3. How is taking the derivative of a vector that describes a curve in space related to taking the derivative (or partial derivatives) of an equation that describes the same curve?